Dandekar_Patterns2020

Dandekar_Patterns2020

A susceptible-infected-recovered (SIR) universal differential equation (UDE) model of the early COVID-19 outbreak in the United Kingdom [1].

Implementation details

The implementation closely follows the original publication, with two differences.

First, the original publication used the model states [S, I, R] as neural network inputs. Here, we use the normalized inputs [S / N, I / N, R / N], where N is the population size. This choice is motivated by the observation that unnormalized inputs are highly multi-scale (e.g. $S \propto 10^7$ while $R \propto 10^3$), leading to large gradients only in the first layer and vanishing gradients in subsequent layers.

Second, we use the Swish activation function instead of ReLU, as this slightly improved training performance.

Other notes

Both training and validation data are provided. The corresponding PEtab-SciML problems can be built using the respective YAML files.

The original study includes data for additional countries [1]. These can be incorporated by replacing the measurement table.

References

1. Dandekar, R., Rackauckas, C., and Barbastathis, G. A machine learning-aided global diagnostic and comparative tool to assess effect of quarantine control in COVID-19 spread. Patterns 1(9), 100145 (2020).